The Solution of the Differential Equation $y ^ { \prime } = x y$

question 31

Multiple Choice

The solution of the differential equation $y ^ { \prime } = x y$ is

• A) \(y = c e ^ { x }\)
• B) \(y = c e ^ { x ^ { 2 } }\)
• C) \(y = c + e ^ { x }\)
• D) \(y = c e ^ { x ^ { 2 } / 2 }\)
• E) \(y = c + e ^ { x ^ { 2 } / 2 }\)

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Definitions:

Marginal Changes

Small, incremental adjustments to an existing plan of action, often considered in decision making and economic analysis.

Other-things-equal Assumptions

A principle in economics which suggests that the effect of one economic variable on another can be determined by holding all other influencing factors constant, commonly referred to as ceteris paribus.

Vertical Intercept

The point at which a line meets the vertical axis of a graph.

Slope

In economics, slope can represent the rate of change between two variables, often used in the context of supply and demand curves.